Physics — Unit 1 — Test 2

N(0,σ^2)

Standard normal N(0,1)

Not normal unless μ=0

N(μ,1)

Not normal unless μ=0

Standard normal N(0,1)

N(μ,1)

N(0,σ^2)

N(0,σ^2)

Not normal unless μ=0

Standard normal N(0,1)

N(μ,1)

Not normal unless μ=0

Standard normal N(0,1)

N(μ,1)

N(0,σ^2)

MGFs never exist for heavy-tailed distributions

MGF determines only the mean and variance

If two MGFs coincide in an open interval around 0, the distributions are identical

The MGF of Normal(0,1) is e^{t}

Exponential(λ)

Gamma(k=λ,θ=1)

Poisson(λ)

Normal(λ,λ)

∇×(∇·F)=0

∇×(∇×F)=0 always

∇(∇·F)=0 always

∇·(∇×F)=0

∇×(φA)=A×∇φ

∇×(φA)=φ∇×A

∇×(φA)=∇(φ)·A

∇×(φA)=∇φ×A+φ(∇×A)

Positively oriented, piecewise smooth, simply connected

Convex only

Self-intersecting

Any region with arbitrary orientation